# test_matrix_exponential

test_matrix_exponential, a C++ code which contains some tests for software that computes the matrix exponential function.

Formally, for a square matrix A and scalar t, the matrix exponential exp(A*t) can be defined as the sum:

exp(A*t) = sum ( 0 <= i < oo ) A^i t^i / i!

The simplest form of the matrix exponential problem asks for the value when t = 1, that is

exp(A) = sum ( 0 <= i < oo ) A^i / i!
Even for this simple case, and for a matrix of small order, it can be quite difficult to compute the matrix exponential accurately.

The code needs the C8LIB and R8LIB libraries.

### Languages:

test_matrix_exponential is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version and a Python version.

### Related Data and Programs:

MATRIX_EXPONENTIAL, a C++ code which demonstrates some simple approaches to the problem of computing the exponential of a matrix.

R8LIB, a C++ code which contains many utility routines using double precision real (R8) arithmetic.

TEST_MAT, a C++ code which defines test matrices.

### Reference:

1. Alan Laub,
Review of "Linear System Theory" by Joao Hespanha,
SIAM Review,
Volume 52, Number 4, December 2010, page 779-781.
2. Cleve Moler, Charles VanLoan,
Nineteen Dubious Ways to Compute the Exponential of a Matrix, SIAM Review,
Volume 20, Number 4, October 1978, pages 801-836.
3. Cleve Moler, Charles VanLoan,
Nineteen Dubious Ways to Compute the Exponential of a Matrix, Twenty-Five Years Later,
SIAM Review,
Volume 45, Number 1, March 2003, pages 3-49.
4. Cleve Moler,
Cleve's Corner: A Balancing Act for the Matrix Exponential,
July 23rd, 2012.
5. Roger Sidje,
EXPOKIT: Software Package for Computing Matrix Exponentials,
ACM Transactions on Mathematical Software,
Volume 24, Number 1, 1998, pages 130-156.
6. Robert Ward,
Numerical computation of the matrix exponential with accuracy estimate,
SIAM Journal on Numerical Analysis,
Volume 14, Number 4, September 1977, pages 600-610.